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This is a direct consequence of a result of Wise (see [14, Theorem I.1.18]), describing each of the two decompositions of certain square complex groups Γ as a fundamental group of a ﬁnite graph of ﬁnitely generated free groups (in the language of the Bass-Serre theory).

Three amalgams with remarkable normal subgroup structures

Let us mention that later a description was given by the Bass-Serre theory, with groups acting on graphs to give geometric intuition: the fundamental group of a graph of groups generalizes both amalgamated products, HNN-extensions and tree products.

On the residual solvability of generalized free products of finitely generated nilpotent groups

Bass et al., 1998) of the fundamental GDH sum-rule.

The Spin Structure of the Proton

It follows that the fundamental group acts on the Bass-Serre tree associated to the graph of groups.

The main theorem of the Bass-Serre theory of groups acting on trees states that a group G acting on a tree T is the fundamental group of a graph of groups whose vertex and edge groups are the stabilizers of certain vertices and edges of T .